What is the meaning of cut off frequency when designing a digital low pass filter for a discret signal

I have a discrete signal captured by an oscilloscope sampled with 10 kS/s. Now I want to design a digital low pass filter to filter the high frequency noise in the signal. I have never learned DSP before, so a lot of things don't seem intuitive to me right now.

I used the simplest filter: b = 0.5; a = [1 b-1]; filter(b, a, Signal);

So, what does b = 0.5 mean? Normalized frequency with respect to what?

Secondly, how does the filter know the frequency of my signal? I didn't tell it that I sampled it with 10 kS/s... It is just an array.

Thanks.

Answer 1

[Honglei Chen]

In this case, b and a together define an IIR filter. b is just the numerator and a is the denominator. The following page may be helpful

http://www.mathworks.com/help/matlab/data_analysis/filtering-data.html

Neither b nor a is related to frequency. At this point, the filter is already designed, and its frequency response is fixed. You can see the corresponding frequency response using

fvtool(b,a,'Fs',10e3)

And you can read the cutoff frequency from the response. In general it is defined at 3dB.

[Bill]

But how does Matlab know the frequency of my signal???

[Honglei Chen]

The filtering operation itself does not care. If you look at the theory, the filter is the same if you sample at 100Hz and cutoff at 20Hz or you sample at 1000Hz and cutoff at 200Hz. So only the ratio between cutoff and sample rate matters. The filter itself merely crunches the numbers. If you want to design a filter, i.e. come up b and a for a given pair of cutoff and sampling frequencies, then you need to use filter design capabilities, such as butter or fir1. HTH